The Cambridge-based troupe has raised its profile over the last year with “Icarus,” which runs at Oberon through May 11, after performances last summer at the Outside the Box festival on Boston Common and at the New York Musical Theatre Festival.

“What do you call Liars & Believers? The phrase I have to use, because I don’t have a better one, is that we are an experimental theater company. But that’s such a fraught term,” Slavick says, “The baggage of ‘experimental theater’ is that it’s weird, inaccessible high-art-for-art’s sake, and that’s not what we do. What we’re doing is just experimenting with all the different ways you can tell a story, in the most engaging and fun way we can come up with.”

The company’s shows can be immersive and even a bit chaotic, but they’ve been building a reputation with offerings such as “Le Cabaret Grimm” and “28 Seeds.” Still, Slavick says, the reaction of theater friends to early Liars & Believers shows tended to be “ ‘I really liked that. But that’s not theater. I don’t know what that is, but that’s not theater.’ Because in some way at that time, the stuff we were doing was seen as too far outside the mainstream.”

He says the evolution of the Boston theater scene since Liars & Believers was founded in 2009 makes him optimistic about the reaction to “Icarus” and beyond. And he gives a lot of the credit for that to two of the town’s biggest theatrical institutions, the American Repertory Theater and ArtsEmerson.

“They have really pushed the doors open wide,” Slavick says. “They’ve reached out and made noise in the mainstream theater community to say, ‘Hey, there’s all kinds of things that are theater.’ ”

“Boston is traditional, it’s been a very traditional community, but that’s breaking way open,” he says. “I hope the work we are doing is changing what people think is included in the word ‘theater.’ ”

“Icarus,” which debuted at the Cambridge YMCA a year ago, transposes the Greek myth to a Depression-era Midwestern traveling sideshow, presented with live performers, puppets, and an onstage band playing Nathan Leigh’s score of slightly tweaked roots music (The New York Times called it “a little Weill, a little Mumford”). Minnie Minoseczeck’s Menagerie of Marvels depends on the inventions of Daedalus to draw a crowd, but trouble ensues when Daedalus’s son, Icarus, falls for Minnie’s daughter and star performer, Penny.

The ensemble includes Jonathan Horvath (Daedalus), Lukas Papenfusscline (Icarus), Aimee Rose Ranger (Minnie), and Liz Tancredi (Penny), with Veronica Barron (everyone else). The band assembled for the show, calling itself Store Bought Absinthe, features Jay Mobley on guitar and music direction, Jenn Bliss on accordion and flute, and Eric Lee on fiddle. Several performers have changed since the premiere, a scene and song have been swapped out for others, and numerous small changes have been made.

“We’re committed to all original work, that’s all we do. It’s not even like people submit plays to us, which we then present,” Slavick says. “We create within the company all the work we do. It is more or less devised collaboratively within the ensemble that actually does the show. We take the source material, and then through improvisations and all different kind of explorations, we create the work.”

Composer Leigh and puppeteer Faye Dupras are very much part of that process, he says.

“The big thing that changed over the past year is, when you’re composing a full-length piece like this, you’re writing more or less song-by-song,” says Leigh. “In the past year, a lot of the work that I’ve done is looking at the show from a big-picture perspective and figuring out how all the little pieces fit together.”

Stylistically, the show was a gamble too, he says. “This is a kind of music that I don’t think is ever really accepted in the theatrical space in an honest way,” Leigh says. “You look at something like ‘Big River’ from the 1980s, where it’s sort of referencing old-time music and folk music but it’s done in a big Broadway way. We’re honestly trying to represent what that music was and how it felt.”

But the audience has gotten it, he says, and that’s a change.

“I lived and worked in New York for a chunk of time, and part of why I left initially was that the work I wanted to be creating was not really accepted. And I’ve definitely seen [a change in] the way people respond to work that is interdisciplinary and narratively experimental,” Leigh says. “People are much more open, much more willing to go with you down the rabbit hole.”

Liars & Believers still attracts a significantly younger audience, primarily in their 20s and 30s, a group that more mainstream theaters are chasing hard, with unclear results. “It’s exciting to me because we’re bringing audiences into the theater who have not been quote-unquote theater audiences,” Slavick says.

One venue that reliably draws that younger audience is Oberon, the ART’s second stage. The ART last fall named Liars & Believers as resident artists at Oberon, along with Touch Performance Art and the Boston Circus Guild. Slavick says that all of them, including the ART, are still figuring out what the three-year residency means, but that it’s already included everything from artist cross-pollination between the companies to ART mentoring on marketing.

Slavick may have to tap more of that expertise. He’s booking touring stops for “Icarus” that could last into spring 2015. Maybe the word is getting out about the evolution here, he says.

At the New York festival, he says, “being from Boston was a great asset. It was really one of our selling points. It’s kind of funny that we were considered in a way exotic, for lack of a better word, for being from Boston. It really was part of how we were marketing and what was touted. ‘Oh, here’s some interesting stuff coming down from Boston. What’s going on up there?’ ”